Average Error: 24.7 → 9.1
Time: 10.6s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.3942487448383101 \cdot 10^{-107} \lor \neg \left(a \le 9.9965607899434403 \cdot 10^{-119}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.3942487448383101 \cdot 10^{-107} \lor \neg \left(a \le 9.9965607899434403 \cdot 10^{-119}\right):\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\

\mathbf{else}:\\
\;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - z)) * ((double) (t - x)))) / ((double) (a - z))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((a <= -2.39424874483831e-107) || !(a <= 9.99656078994344e-119))) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) (a - z)))) * ((double) (t - x))))));
	} else {
		VAR = ((double) (t + ((double) (((double) (y / z)) * ((double) (x - t))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original24.7
Target11.9
Herbie9.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.3942487448383101e-107 or 9.9965607899434403e-119 < a

    1. Initial program 22.7

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]

    2. Simplified11.0

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\]
    3. Using strategy rm

    4. Applied clear-num11.3

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}}\]
    5. Using strategy rm

    6. Applied associate-/r/11.0

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{a - z} \cdot \left(t - x\right)\right)}\]

    7. Applied associate-*r*8.7

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{a - z}\right) \cdot \left(t - x\right)}\]

    8. Simplified8.6

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z}} \cdot \left(t - x\right)\]

    if -2.3942487448383101e-107 < a < 9.9965607899434403e-119

    1. Initial program 29.5

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]

    2. Simplified24.4

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\]

    3. Taylor expanded around inf 15.4

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]

    4. Simplified10.4

      \[\leadsto \color{blue}{t + \frac{y}{z} \cdot \left(x - t\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.3942487448383101 \cdot 10^{-107} \lor \neg \left(a \le 9.9965607899434403 \cdot 10^{-119}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))